Operator Inequalities
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Operator Inequalities
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Author : Schroder
language : en
Publisher: Academic Press
Release Date : 1980-09-01
Operator Inequalities written by Schroder and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-09-01 with Computers categories.
Operator Inequalities
Operator Inequalities Of The Jensen Eby Ev And Gr Ss Type
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Author : Silvestru Sever Dragomir
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-12
Operator Inequalities Of The Jensen Eby Ev And Gr Ss Type written by Silvestru Sever Dragomir and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-12 with Mathematics categories.
The main aim of this book is to present recent results concerning inequalities of the Jensen, Čebyšev and Grüss type for continuous functions of bounded selfadjoint operators on complex Hilbert spaces. In the introductory chapter, the author portrays fundamental facts concerning bounded selfadjoint operators on complex Hilbert spaces. The generalized Schwarz’s inequality for positive selfadjoint operators as well as some results for the spectrum of this class of operators are presented. This text introduces the reader to the fundamental results for polynomials in a linear operator, continuous functions of selfadjoint operators as well as the step functions of selfadjoint operators. The spectral decomposition for this class of operators, which play a central role in the rest of the book and its consequences are introduced. At the end of the chapter, some classical operator inequalities are presented as well. Recent new results that deal with different aspects of the famous Jensen operator inequality are explored through the second chapter. These include but are not limited to the operator version of the Dragomir-Ionescu inequality, the Slater type inequalities for operators and its inverses, Jensen’s inequality for twice differentiable functions whose second derivatives satisfy some upper and lower bound conditions and Jensen’s type inequalities for log-convex functions. Hermite-Hadamard’s type inequalities for convex functions and the corresponding results for operator convex functions are also presented. The Čebyšev, (Chebyshev) inequality that compares the integral/discrete mean of the product with the product of the integral/discrete means is famous in the literature devoted to Mathematical Inequalities. The sister inequality due to Grüss which provides error bounds for the magnitude of the difference between the integral mean of the product and the product of the integral means has also attracted much interest since it has been discovered in 1935 with more than 200 papers published so far. The last part of the book is devoted to the operator versions of these famous results for continuous functions of selfadjoint operators on complex Hilbert spaces. Various particular cases of interest and related results are presented as well. This book is intended for use by both researchers in various fields of Linear Operator Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.
Operator Inequalities Of Ostrowski And Trapezoidal Type
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Author : Silvestru Sever Dragomir
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-08
Operator Inequalities Of Ostrowski And Trapezoidal Type written by Silvestru Sever Dragomir and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-08 with Mathematics categories.
Inequalities of Ostrowski and Trapezoidal Type for Functions of Selfadjoint Operators on Hilbert Spaces presents recent results concerning Ostrowski and Trapezoidal type inequalities for continuous functions of bounded Selfadjoint operators on complex Hilbert spaces. The first chapter recalls some fundamental facts concerning bounded Selfadjoint operators on complex Hilbert spaces. The generalized Schwarz’s inequality for positive Selfadjoint operators as well as some results for the spectrum of this class of operators are presented. The author also introduces and explores the fundamental results for polynomials in a linear operator, continuous functions of selfadjoint operators that will play a central role throughout the book. The following chapter is devoted to the Ostrowski’s type inequalities, which provide sharp error estimates in approximating the value of a function by its integral mean and can be used to obtain a priory error bounds for different quadrature rules in approximating the Riemann integral by different Riemann sums. The author also presents recent results extending Ostrowski inequality in various directions for continuous functions of selfadjoint operators in complex Hilbert spaces. The final chapter illustrates recent results obtained in extending trapezoidal type inequality in various directions for continuous functions of selfadjoint operators in complex Hilbert spaces. Applications for mid-point inequalities and some elementary functions of operators as also provided. This book is intended for use by researchers in various fields of Linear Operator Theory and Mathematical Inequalities. As well as postgraduate students and scientists applying inequalities in their specific areas.
Intelligent Comparisons Ii Operator Inequalities And Approximations
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Author : George A. Anastassiou
language : en
Publisher: Springer
Release Date : 2017-01-13
Intelligent Comparisons Ii Operator Inequalities And Approximations written by George A. Anastassiou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-13 with Technology & Engineering categories.
This compact book focuses on self-adjoint operators’ well-known named inequalities and Korovkin approximation theory, both in a Hilbert space environment. It is the first book to study these aspects, and all chapters are self-contained and can be read independently. Further, each chapter includes an extensive list of references for further reading. The book’s results are expected to find applications in many areas of pure and applied mathematics. Given its concise format, it is especially suitable for use in related graduate classes and research projects. As such, the book offers a valuable resource for researchers and graduate students alike, as well as a key addition to all science and engineering libraries.
Operator And Norm Inequalities And Related Topics
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Author : Richard M. Aron
language : en
Publisher: Springer Nature
Release Date : 2022-08-10
Operator And Norm Inequalities And Related Topics written by Richard M. Aron and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-10 with Mathematics categories.
Inequalities play a central role in mathematics with various applications in other disciplines. The main goal of this contributed volume is to present several important matrix, operator, and norm inequalities in a systematic and self-contained fashion. Some powerful methods are used to provide significant mathematical inequalities in functional analysis, operator theory and numerous fields in recent decades. Some chapters are devoted to giving a series of new characterizations of operator monotone functions and some others explore inequalities connected to log-majorization, relative operator entropy, and the Ando-Hiai inequality. Several chapters are focused on Birkhoff–James orthogonality and approximate orthogonality in Banach spaces and operator algebras such as C*-algebras from historical perspectives to current development. A comprehensive account of the boundedness, compactness, and restrictions of Toeplitz operators can be found in the book. Furthermore, an overview of the Bishop-Phelps-Bollobás theorem is provided. The state-of-the-art of Hardy-Littlewood inequalities in sequence spaces is given. The chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.
Positive Definiteness Of Functions With Applications To Operator Norm Inequalities
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Author : Hideki Kosaki
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-06-10
Positive Definiteness Of Functions With Applications To Operator Norm Inequalities written by Hideki Kosaki and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-10 with Mathematics categories.
Positive definiteness is determined for a wide class of functions relevant in the study of operator means and their norm comparisons. Then, this information is used to obtain an abundance of new sharp (unitarily) norm inequalities comparing various operator means and sometimes other related operators.
Inequalities For The Numerical Radius Of Linear Operators In Hilbert Spaces
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Author : Silvestru Sever Dragomir
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-14
Inequalities For The Numerical Radius Of Linear Operators In Hilbert Spaces written by Silvestru Sever Dragomir and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-14 with Mathematics categories.
Aimed toward researchers, postgraduate students, and scientists in linear operator theory and mathematical inequalities, this self-contained monograph focuses on numerical radius inequalities for bounded linear operators on complex Hilbert spaces for the case of one and two operators. Students at the graduate level will learn some essentials that may be useful for reference in courses in functional analysis, operator theory, differential equations, and quantum computation, to name several. Chapter 1 presents fundamental facts about the numerical range and the numerical radius of bounded linear operators in Hilbert spaces. Chapter 2 illustrates recent results obtained concerning numerical radius and norm inequalities for one operator on a complex Hilbert space, as well as some special vector inequalities in inner product spaces due to Buzano, Goldstein, Ryff and Clarke as well as some reverse Schwarz inequalities and Grüss type inequalities obtained by the author. Chapter 3 presents recent results regarding the norms and the numerical radii of two bounded linear operators. The techniques shown in this chapter are elementary but elegant and may be accessible to undergraduate students with a working knowledge of operator theory. A number of vector inequalities in inner product spaces as well as inequalities for means of nonnegative real numbers are also employed in this chapter. All the results presented are completely proved and the original references are mentioned.
Operator Inequalities
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Author : Johann Schröder
language : en
Publisher:
Release Date : 1980
Operator Inequalities written by Johann Schröder and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Inequalities (Mathematics) categories.
Schr Dinger Operators Eigenvalues And Lieb Thirring Inequalities
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Author : Rupert L. Frank
language : en
Publisher: Cambridge University Press
Release Date : 2022-11-30
Schr Dinger Operators Eigenvalues And Lieb Thirring Inequalities written by Rupert L. Frank and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-30 with Mathematics categories.
Takes readers from the very basic facts to the most recent results on eigenvalues of Laplace and Schrödinger operators.
Advances In Mathematical Inequalities
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Author : Shigeru Furuichi
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-01-20
Advances In Mathematical Inequalities written by Shigeru Furuichi and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-20 with Mathematics categories.
Mathematical inequalities are essential tools in mathematics, natural science and engineering. This book gives an overview on recent advances. Some generalizations and improvements for the classical and well-known inequalities are described. They will be applied and further developed in many fields. Applications of the inequalities to entropy theory and quantum physics are also included.